A "Fresnel phase zone plate" is similar in appearance to a conventional Fresnel lens, in that it comprises several concentric rings, which from the side look like a series of sawtooth-shaped ridges. However, the phase element is based on diffraction rather than refraction and has many more zones and a much smaller difference in height between adjacent zones compared to a conventional Fresnel lens, with a typical height difference of a phase zone lens element corresponding to a phase change of only 2.pi. (one wavelength). It is typically produced by etching or machining the ridges into a surface, which may be a thin sheet of transparent material, or the spherical surface of a conventional refractive lens. A kinoform is a generalized form of Fresnel phase zone plate having an arbitrary phase profile, for example the interference pattern defined by two arbitrary coherent point sources on an arbitrary surface, to which an arbitrary 2-dimensional phase profile defined by an arbitrary polynomial may be added. In particular, a Fresnel phase zone plate may be defined by the interference pattern produced on a flat plane normal to the optical axis defined by the two points, with one point at infinity.
Diffraction efficiency for a given diffraction order is a measure of how much light goes into that order as opposed to all the other diffraction orders. Fresnel phase zone plates can provide a very high diffraction efficiency, at least in the first diffraction order. The spacing between adjacent zones of a conventional kinoform lens is not constant, but grows smaller as the distance from the optical axis increases; however, the grating height of each ridge, called the surface relief height, which is the distance between the highest point and the lowest point of the same zone (or of two adjacent zones) is usually constant. For collimated light at the design wavelength that is incident on the phase zone lens element in a normal direction, essentially all of the light will be diffracted in a direction corresponding to the first diffraction order.
The zones in a kinoform typically take the form of circular annular rings; however the zones may assume other shapes, such as bars (as in a conventional spectrographic grating) and ellipses (to produce different focal lengths at different angular orientations about the optical axis). Moreover, groups of zones may be arranged in a two-dimensional cellular array, with each cell functioning as an individual optical element. Within each zone, the theoretically optimal depth profile is a smooth curve extending continuously from a highest region to a lowest region; however for ease of manufacturablity, the optimal profile may be approximated as a series of steps (phase levels) each of constant depth.
Theoretical constraints limit the diffraction efficiency obtainable from either continuous or multi-level diffractive optical elements. Assuming that the underlying assumptions for the "scalar diffraction theory" (the incident light is bent by a small angle and the diffracted field is observed far from the diffraction structure), the "Fresnel approximation" (a spherical wave can be approximated by a quadratic) and "Fraunhofer diffraction" (the quadratic phase terms can be ignored) are all valid, the diffraction efficiency .eta..sub.q.sup.n of the q.sup.th order of an N-level diffraction zone is: ##EQU1## where .phi. is the phase depth change (in waves) of each subperiod (phase level) and .phi..sub.o =.phi..multidot.N is the total phase depth change (in waves) within each zone.
For an infinite number of phase levels N, this equates to: ##EQU2##
Thus, at least when the above assumptions are valid, the diffraction efficiency of the q.sup.th diffraction order can be approximated as a function which depends only on the number of phase levels N in each zone and the phase shift (in waves) (represented by .phi..sub.o); in accordance with the above equations, for first order diffraction (q=1), the theoretical maximum (100%) corresponds to a phase shift of one wave (.phi..sub.o =1).
Applying Snell's law to the case of a stepped diffraction plate formed from an optical material having an index of refraction n surrounded by air and a step height of .delta.d (measured in the normal direction), the effective phase height .phi. of each step is a function of the angle .theta. by which the incident light deviates from the normal of the surface: ##EQU3##
Thus, KOE diffraction efficiency for a phase zone plate having a given number of steps each of a predetermined height depends not only on wavelength and refractive index, but also on incident angle.
Although a solitary diffractive lens is generally not suitable for use over a wide range of wavelengths, diffractive lens elements have been used to compensate for aberrations inherent in spherical refractive elements in broadband applications in both the visible and the infrared spectra. Combining kinoform (diffractive) and optical (refractive or reflective) elements generally reduces the number of optical elements by one third and requires no special glass materials for secondary chromatic aberration correction.